Celeste Corcoran and her daughter Sydney are recovering together after both were critically injured in the Boston Marathon attacks

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The thought of death drifted, for a moment, into the mind of Celeste Corcoran as she lay critically wounded on the sidewalk near the finish line of the Boston Marathon last month. The wife and mother would have to have both legs amputated below the knee. When the thought arrived, though, she rejected it.

"I just kept saying over and over again in my head, no, no," Corcoran, 47, said in an interview with the "Today" show's Natalie Morales. "I just remembered thinking, I don't want to leave my family. There's just too much to do."

Photos: Boston Marathon Blasts

In Boston Medical Center, where she was recovering beside her 18-year-old daughter, who was also critically wounded in the attack, Corcoran focused on what she kept, rather than what she lost in the attack.

"I like my legs, but if I can get a new set of legs and still be here and go through the milestones—her graduation," she said, motioning toward her daughter. "I have an older son I'm so close to. I just want to see everything in their lives," she said. "I'm not ready to leave."

Her daughter Syndey, who is expected to fully recover after shrapnel from the blast severed an artery in her leg, had a similar attitude.

"I knew I at least had my mother. So really, the legs don't mean anything to me," she told Morales. "I know it's hard for her, but I'm glad I have her."

Celeste's sister Carmen Acabbo, who was running the Marathon when the bombs exploded, said the bond between her sister and niece had always been strong and was helping them through their recoveries.

"They have the best relationship," she said. "They are like joined at the hip. They are like the mother and daughter that anyone who has a daughter wants to emulate."

The pair has received an outpouring of support from friends, family and perfect strangers who have visited, sent gifts and donated to the family's medical fund. Celeste was brought to tears by a visit from Marines who walked into her hospital room on prosthetic legs and told her inspiring stories about their own recoveries. "This," one Marine said, waving his hand over her legs, "is just a change in scenery."

Celeste said she is determined to go back to work as a hairdresser after she is fitted with prosthetic legs, while her daughter hopes to finish her senior year of high school and go onto college.

In the meantime, she's happy to have the love and support of her husband, son, other family members and, of course, her daughter.

"We're all here, we're all alive, I've got my baby with me, I couldn't ask for more," she said.